Poisson limits for \(U\)-statistics.

DOI10.1016/S0304-4149(01)00153-3zbMath1059.60063MaRDI QIDQ1766076

Thomas Mikosch, Herold G. Dehling, André Robert Dabrowski, Olimjon Sh. Sharipov

Publication date: 25 February 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

zbMATH Keywords

point processesstable distributions\(U\)-statisticscorrelation dimension

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Extreme value theory; extremal stochastic processes (60G70) Stable stochastic processes (60G52) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (5)

Limit theorems for Betti numbers of extreme sample clouds with application to persistence barcodes ⋮ On Sevast'yanov's theorem ⋮ Topological crackle of heavy-tailed moving average processes ⋮ Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to \(U\)-statistics and stochastic geometry ⋮ Limit Theorems for Moving Averages with Random Coefficients and Heavy-Tailed Noise

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• Short distances, flat triangles and Poisson limits
• Consistency of Hill's estimator for dependent data
• Strong laws for 𝐿- and 𝑢-statistics

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